The simplest example of a tiling of the plane is formed by taking squares of side length 1 with full edge-to-edge contact. If you slide such a tiling in the direction of an edge by an integer distance, the tiling overlays itself exactly. Such a tiling is said to be periodic.
Here all tiles are the same and consist of isosceles triangles with apex angle , where is the order of symmetry around the center. The triangles are white and either one or two other colors.
You can vary the symmetry order and the number of layers around the center.
Although this tiling is not periodic (except for symmetry order 3), there are arbitrarily large pieces of it that look periodic. The full definition of an aperiodic tiling rules that out.